A248888 Numbers k such that prime(k) <= 2*sigma(k).

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 24, 28, 30, 36, 40, 42, 48, 60, 72, 84, 90, 96, 120, 180

Offset: 1

Author

Farideh Firoozbakht, Oct 17 2014

Keywords

• nonn
• fini
• full

Comments

Obviously only for n = 1, prime(n) = 2*sigma(n).

It is interesting that all terms of the sequence A112587 are in the sequence and this sequence has only two more terms 96 & 180. Hence if phi(n) <= 2*tau(n) then prime(n) <= 2*sigma(n).

Crossrefs

Cf, A000005, A000010, A000040, A000203.

Programs

Mathematica

Select[Range[200], Prime[#] <= 2DivisorSigma[1,#]&]